Lepton-Hadron Collider Physics and Detectors : Electron Ion Collider (EIC)
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Lepton-Hadron Collider Physics and Detectors :
Electron Ion
√ Collider (EIC)
ep at s > 1 TeV
G. Fleming1 , E. Kinney2 , S. Lammers3 , S. Magill4
1
Ohio State University, Columbus, Ohio
2
University of Colorado, Boulder, Colorado
3
University of Wisconsin, Madison, Wisconsin
4
Argonne National Laboratory, Argonne, Illinois
Abstract
Consider the physics opportunities of a lepton-hadron collider and how
these opportunities might be realized in a possible polarized eRHIC facility
and an e-p collider as part of a staged or final version VLHC. Detector
challenges should be considered including possible physics opportunities
in the forward direction. Contrast these opportunities with the physics
likely from existing facilities and identify R&D needs for a realization of
future programs.
1 Introduction
The Deep Inelastic Scattering (DIS) process, in which an electron (or any lepton)
is used to destructively probe a hadron has proven to be one of the best ways
to study hadronic structure and the nature of the strong interactions between
its fundamental constituents (quarks and gluons). Over the past 30 years, the
theory of color interactions of quarks and gluons, Quantum Chromodynamics
(QCD), has been validated to distances at least 10 times smaller than the size
of the proton. A future e-p collider has the following attractive advantages :
• The (pointlike) electron probe is ideal for examining proton structure.
• It is tunable over a wide range in hard scattering scale.
• QCD parameters and properties can be studied in a relatively background
free environment.
• Some unique couplings may exist to new physics at high energy.
The first three points, taken together, define an e-p collider as a ”QCD Fac-
tory” where all aspects of the strong interaction can be investigated, including
short- to long-distance interactions between quarks and gluons, low- to high-
density partonic states, and detailed measurements of the proton structure and
its evolution.
12 Electron-Ion Collider (EIC)
At 2 recent Town Meetings held at JLAB in December 2000 and at BNL in
January 2001, it was recommended to the Nuclear Sciences Advisory Committee
(NSAC) that a high-luminosity electron-ion collider covering CM energies in the
range of 30-100 GeV be built as the next generation facility for the study of
electromagnetic and hadronic physics [1]. The purpose of this collider would be
to answer the following questions :
• What is the structure, both flavor and spin, of hadrons in terms of their
quark and gluon constituents?
• How do quarks and gluons evolve into hadrons via the dynamics of con-
finement?
• How do quarks and gluons reveal themselves in the structure of atomic
nuclei?
In addition to these questions, the Electron-Ion Collider will contribute to
a fundamental understanding of QCD by testing its predictions and parame-
ters in extreme conditions and at the limits of its expected applicabilities. In
particular, parton distributions will be measured in regions of parameter space
in which non-linear effects are expected to dominate. Tests of QCD in regions
where many-body effects between strongly-interacting matter are expected will
be done. An even more fundamental question is whether nuclei can be used to
study partonic matter under extreme conditions.
2.1 EIC Parameters
The EIC should be built with the following characteristics :
• Capable of collisions between electrons (positrons) and protons, light and
heavy nuclei
• Provide high luminosity L ≥ 1033 cm−2 s−1 per nucleon
• Operate in a wide range of CM energies Ecm = 15 GeV → 100 GeV
• Polarization of electron and proton spins
• Two interaction regions with dedicated detectors
2.2 EIC Physics Priorities
The following list of physics topics related to QCD can be addressed at the EIC
:
Flavor and Spin Structure of the Nucleon : It will be possible to
measure the pdfs of light quarks and the gluon by tagging final states in inclusive
2DIS. For example, by tagging kaons, both momentum and spin pdfs of strange
quarks can be determined with high precision down to x ' 10−3 . In general,
the spin structure of the nucleon can be determined to lower x than is presently
known, leading to a better understanding of the contribution of the sea to the
total spin of the nucleon. Finally, a complete understanding of the partonic
structure of a nucleon requires not only momentum and spin contributions, but
also those from, for example, parton-parton correlations. These fall into a class
of structure functions called Generalized Parton Distributions, many of which
can be accessed at the EIC.
Partonic Substructure of Mesons and Hyperons : Very little is known
about the structure of hyperons and mesons, despite their role as the glue that
holds nuclei together. At the EIC, measurements of the quark and gluon struc-
ture of these particles can be compared to those in the nucleon. Since mesons
and hyperons are the Goldstone bosons of spontaneously broken chiral symme-
try, fundamental questions of the role of quarks and gluons in transition from
partonic degrees of freedom to their Goldstone modes can also be addressed.
Hadronization : At the EIC, complete final states of the hard scattering
process can be detected and reconstructed, allowing studies to be done of the
transformation by colored quarks and gluons into color neutral hadrons. This
non-perturbative process must be measured experimentally in order to under-
stand the long-range dynamics of confinement. Using flavor tagging and jet
reconstruction, studies of the transfer of spin from quarks to hadronic final
states can also be done.
Role of Quarks and Gluons in Nuclei : Comparisons of collisions in-
volving both light and heavy nuclei at the EIC can illustrate possible effects of
nuclear matter on the parton distributions, for example, the effects of nuclear
binding, expressed as exchanged mesons, on the underlying quarks and gluons
in nucleons. The large range in x at the EIC allows the x-dependence of these
and other nuclear effects to be determined. Also, the initial conditions for rela-
tivistic heavy ion collisions can be determined, helping to fill in missing pieces
of the transition from cold, partonic matter to a hot, dense quark-gluon plasma.
High Density QCD at Low x : At HERA, the scaling dependence of
F2 at low x indicates that the gluon density increases very steeply as x de-
creases. Unitarity bounds on the gluon distribution predict that this steep rise
must eventually saturate, at around x ' 10−6 for Q2 = 10 GeV 2 . Across this
boundary, non-linear evolution of parton distributions occurs, leading to a new
state of color-saturated high-density QCD. Since the parton densities in nuclei
are enhanced by a factor of A1/3 , these effects might be seen in nuclei at lower
energies than in protons. The EIC could be the first place to see this new state
of partonic matter, if nuclear effects are negligible or non-existent in the low x
region.
3√
3 ep at s > 1 TeV
√
There are presently no e-p colliders planned at s > 1 TeV. A possible upgrade
to HERA, THERA [2], in which 250 GeV electrons from TESLA [3] are collided
√
with 900 GeV protons from HERA, has been studied. This option (at s ∼ 1
TeV) can only be realized if TESLA is built at DESY, if the accelerators are
made to match at an appropriate IP, and if luminosity is taken from the TESLA
program and provided for THERA.
At the Snowmass 2001 workshop, studies were made of an e-p option in
which electrons from a future e+ e− linear collider are collided with protons
from a future VLHC [4]. Our ”standard” option was defined as a 250 GeV
e− interacting with a 20 TeV proton, corresponding to Stage √ I of the VLHC
(epVLHC). The corresponding CM reach of this option is s ∼ 4.5 TeV. The
ratio of incoming beam energies is Ep /Ee = 80, more than twice the asymmetry
at HERA. As an alternative, one of the THERA options, 800 GeV e x 800 GeV
p was studied as an example of a symmetric collider. Both the asymmetry of the
beams and the physics requirements affect the design of detectors at a future
e-p facility.
3.1 Physics Priorities
In the early planning for HERA, it was thought that new physics beyond the
Standard Model was within range. HERA would see at least some of the fol-
lowing : leptoquarks, excited electrons, contact interactions indicating quark
substructure, SUSY, and others. Now we know that the Standard Model is
alive and well at HERA. However, HERA has expanded our knowledge of the
proton structure by several orders of magnitude in both hard scattering scale,
Q2 , and longitudinal momentum fraction, x. It has shown that the inclusive
proton structure function, F2 , rises steeply as x decreases. This steep rise has
been linked to a large increase in the gluon distribution in the proton at low x.
HERA has also discovered that hard diffractive scattering contributes a signifi-
cant amount to the total DIS cross section. Also, at HERA, extensive inclusive
and exclusive measurements have been made to test the limits of perturbative
QCD and to study the transition to the non-perturbative regime.
So, we have learned that e-p at HERA is an ideal place to study the dynamics
of perturbative QCD. We have, therefore, taken this lesson from HERA and
applied it to our determination of physics priorities at a future e-p collider. We
believe that the following ordered physics priorities should form the basis of the
physics case for a future e-p collider.
3.1.1 Perturbative QCD Dynamics at Low x
Th evolution of partons in the proton is normally described by a set of lin-
ear equations where the number of partons evolves as a function of either Q2
4(DGLAP evolution), x (BFKL evolution), or a combination of both Q2 and x
evolution (DLLA). The following table summarizes the forms of linear parton
evolution :
DGLAP DLLA BFKL
Resummed terms (αs ln Q2 )n (αs ln Q2 ln 1/x)n (αs ln 1/x)n
Region High/medium x low x small x limit
Program Fixed target DIS HERA/THERA epVLHC
Outstanding questions remain about the form of the linear evolution pro-
cesses seen in the HERA DIS data. At HERA, DGLAP alone can describe the
full range of inclusive F2 data as long as enough gluons are included in the
proton at a low scale. Some more exclusive measurements, e.g., final state mul-
tiplicities in the current region of the Breit frame, are consistent with DLLA
evolution, and from forward jets and hadrons, it also appears that DGLAP
alone is unable to describe the data. The tunability of the electron probe is a
distinct advantage in measurements of this type, since it allows for selection of
extreme kinematic regions where one evolution scheme is expected to dominate
over the others.
A future e-p collider at very high energy can access the very small x region
where BFKL evolution should apply. At some point, DGLAP should fail to
describe the data when large longitudinal distances are being probed (very small
x). As the number of partons increases, which is evident at HERA with no signs
of stopping, eventually parton-parton interactions should start to occur. The
eventual trade-off between parton evolution and parton-parton recombination
”saturates” the cross section and the steep rise becomes flat. The complete
description of parton evolution would then require the addition of non-linear
terms. This should occur when the number of gluons is xg ∼ Q2 /αs (Q2 ).
HERA has had much success in mapping the low-x growth in F2 , but has not
yet seen effects that could be interpreted as saturation of the proton structure
function. Extrapolating with GRV pdfs, at Q2 = 10 GeV 2 , the saturation
boundary would occur at x ' 10−6 .
At Snowmass, simulated events were generated using the CASCADE Monte
Carlo program [5] which incorporates the CCFM parton evolution model. This
model should be a good choice at a future e-p collider since it allows for x-
evolution of the partons (BFKL) in the small x limit. Figure 1 shows the e-p
scattering kinematic plane in x and Q2 comparing HERA with THERA and
epVLHC. A minimum scattering angle for the electron of 10o was required for
each option and shows up as the high x, low Q2 limit of the events generated
for THERA and epVLHC. The low x, high Q2 limit is the kinematic constraint,
y ≤ 1. The red shaded region denotes the part of the region where ln 1/x is at
least a factor of 5 larger than ln Q2 . For Q2 = 10 GeV 2 , this is where saturation
effects should occur.
The onset of saturation is also affected by the twist level (higher order
5Q**2 (GeV**2)
3
10
2
10
10
-6 -5 -4 -3 -2
10 10 10 10 10
x
Figure 1: Kinematics at HERA, THERA, and epVLHC, indicating where satu-
ration is expected to occur.
(1/Q2 )n terms of the evolution equations. Current measurements of F2 are well-
described by twist-2 evolution equations, but even after considering higher-order
corrections these equations do not lead to saturation as x → 0. However, with
appropriate choices of pdfs and screening radius (size of the region in the proton
in which parton-parton interactions begin to occur), twist-4 contributions to the
evolution equations predict the onset of saturation at around x = 10−7 .
At even lower x, beyond the saturation boundary, perturbation theory breaks
down even if αs is small, because the non-linear effects are large. The physical
state of quarks and gluons in this region has been described as a Color-Glass
Condensate, named from the type of equations used to describe high-density
concentrations of the colored
√ gluons. If this state exists, it should be seen at a
future e-p collider with s in the few TeV range.
3.1.2 Proton Structure and Flavor Decomposition
In addition to measurements of inclusive proton structure functions, an e-p
collider is also an ideal place to decompose the inclusive F2 measurement into
individual flavor pdfs. In searches for new physics at p-p machines, e.g., at the
LHC and VLHC, it will be important to know the contribution to cross section
measurements from the heavy quark content of the proton. As is the case today,
all measurements of the b quark cross section, including those at HERA, are
6larger than the predicted theoretical values, and without a precise measure of
the b content of the proton, this difference is hard to interpret as new physics.
Comparisons between HERA, THERA, and epVLHC for heavy quark dis-
tributions were examined in MC simulated events. The following plots show
the light and heavy quark distributions in pseudorapidity (η) for the three e-p
options. A minimum pT requirement of 6 GeV was made on the quarks. For
Quark η Distributions
dσdη (nb)
10
HERA
u,d,s quarks
1 c quarks
b quarks
-1
10
-2 pT 5 GEV
10
-8 -6 -4 -2 0 2 4 6 8 10
Pseudorapidity
dσ/dη (nb)
-1
10
THERA
-2
10
-8 -6 -4 -2 0 2 4 6 8 10
Pseudorapidity
10
dσ/dη (nb)
epVLHC
1
-1
10
-2
10
-8 -6 -4 -2 0 2 4 6 8 10
Pseudorapidity
Figure 2: η distributions of quarks at HERA, THERA, and epVLHC.
both HERA and epVLHC, the quarks are forced into the forward (proton di-
rection) region, requiring a detector which would look more like a fixed target
detector than a collider detector. However, for the symmetric case of THERA,
the quarks are scattered closer to the central region. A ”standard” symmet-
ric collider detector with vertex detector and some extended coverage in the
forward region might work for this configuration.
3.1.3 Beyond the Standard Model (BSM)
Although the opportunities for studying exotic physics at a future e-p facility
are potentially rich and varied, we did not attempt any predictive studies at
Snowmass. However, the following discussion summarizes the current state
of some BSM investigations and indicates where a future e-p collider could
contribute.
Leptoquarks (LQ) and squarks : An e-p collider is ideal for the produc-
tion of new bosons possessing both leptonic and baryonic quantum numbers,
7e.g., leptoquarks and squarks in SUSY with R-parity violation. HERA has set
limits on the production of these particles that are competitive with comparable
limits set at the Tevatron. If LQs are discovered in a hadron-hadron collider
(e.g. LHC), a future e-p collider would be the best place to study their proper-
ties : the angular distribution of the final-state lepton can discriminate between
scalar and vector resonances; the LQ fermion number is determined by compar-
ing the signal cross section in e+ p and e− p collisions; the chirality structure of
the LQ coupling can be determined by the polarisation of the incoming lepton
beam. Further constraints on the LQ coupling can be made by polarizing the
proton beam as well. At an e-p facility at the VLHC, s-channel LQ resonances
in the mass range up to ∼ 4.5 T eV could be seen directly, as well as higher mass
states by parametrisation as a contact interaction.
Contact Interactions : In addition to very high mass LQs, generic four-
fermion contact interactions can also signal new physics processes, e.g., by in-
terfering with the observed NC DIS cross section. If contact interactions were
seen, e-p collisions would give a unique insight into the chiral structure of the
interactions by exploiting the lepton beam polarization.
Excited Leptons : Although the LHC will be able to discover e∗ and
ν by pair production independent of coupling, some processes involving these
∗
particles are better done at an e-p collider. For example, searches for ν ∗ can
take advantage of the large u-quark density in the proton and the helicity nature
of the charged-current interaction.
Large Extra Dimensions : The t-channel exchange of Kaluza-Klein gravi-
tons in models with large extra dimensions affects the Q2 distribution of NC
DIS events. While the LHC again can probe very large compactification scales,
some models predict that fermions with different gauge quantum numbers are
localised on different branes. A future e-p machine could provide complemen-
tary information on fermion localization, since the two-gluon final state would
dominate the cross section at the LHC.
3.2 Detector Considerations
Since it is easier to accelerate
√ protons to higher energy than electrons and
positrons, the highest s e-p machines would be highly asymmetric in incoming
beam energies. At HERA, the proton beam energy is ∼ 30× that of the lepton
beam. At the VLHC, with 20 T eV protons colliding with e+ e− linear collider
electrons of 250 GeV , the asymmetry factor is ∼ 80. Therefore, the detector
must be highly asymmetric with most of the detection capability far forward
in the proton direction. The detection of scattered electrons would also require
calorimetry in the opposite direction to the proton. For studies of QCD dy-
namics and non-linear evolution effects, an asymmetric detector would suffice,
including good angle and energy measurement of the scattered electron and the
capbility of hadron/jet reconstruction in the far forward region. Since the ob-
jective is an inclusive measurement at extremely low x, a split detector of this
8type would be necessary at such a highly asymmetric collider facility.
For measurements of flavor pdfs, a more symmetric configuration would√be
desirable, however, as already mentioned, this would come at the expense of s.
Even with symmetric beam energies, the heavy quarks populate the forward
region of the detector, so forward detection is still important. Detectors for
more symmetric beams look more like traditional collider detectors.
For studies of possible BSM processes, it is important to have a hermetic 4π
detector. This is very difficult to do with highly asymmetric beams, so specific
BSM searches would be chosen at the detector design stage. This limits the
effectiveness of a future e-p machine as a BSM search device, hence our lower
priority for this type of physics.
4 Conclusions
We have attempted to understand √ the important physics issues for possible fu-
ture e-p colliders. Both the low s (EIC) and high energy options (epVLHC)
are seen primarily as QCD ”Factories” which utilize the advantages of a point-
like, well-defined probe to measure the parameters and dynamics of QCD theory.
Our aim was to provide a general, first view of future e-p options, so that if, at
some future date, an e-p collider configuration becomes viable, specific physics
and detector studies can build on our ideas as contained here.
References
[1] The Electron-Ion-Collider, White Paper submitted to the NSAC Long
Range Planning Meeting, March 2001.
[2] The THERA Book, December 2001,
http://www.ifh.de/thera/tbook/index.html.
[3] TESLA Technical Design Report, DESY 2001-011, March 2001.
[4] The Very Large Hadron Collider (VLHC), http://www.vlhc.org/.
[5] Hannes Jung, The CCFM Monte Carlo Generator CASCADE, DESY-
01-114, LUNFD6-NFFL-7202-2001, Sep 2001. 14pp. Submitted to Com-
put.Phys.Commun., e-Print Archive: hep-ph/0109102
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